Device for generating function of approximate n-th degree and temperature compensation quartz oscillation circuit

ABSTRACT

A circuit for generating a component of n-th order includes: six differential amplifiers ( 15 A to  15 F) having a pair of input terminals supplied with a common linear input signal and a constant level signal of a predetermined level, outputting a reversed or non-reversed signal to the linear input signal, and having a limiter function to limit the output signal to a predetermined maximum value and a minimum value; a constant level signal generation circuit for supplying the constant level signal to each of the six differential amplifiers; a current mirror circuit ( 14 ) for controlling current flowing in the differential amplifiers ( 15 A to  15 F); and addition resistors ( 16 A,  16 B) for adding the output current of the differential amplifiers ( 15 A to  15 F). By increasing the flowing current by the sixth differential amplifier ( 15 F) so as to increase the resistance value, it is possible to obtain a highly accurate output current of a component of a 5-th order function having more precipitous inclination with respect to the input signal.

TECHNICAL FIELD

The present invention relates to an approximate n-th order functiongenerating device for generating a function of an approximate n-th orderand a temperature compensation crystal oscillation circuit using thedevice.

BACKGROUND ART

As for a crystal resonator of an AT cut often used for a crystaloscillator, it is known that a temperature change against a fixednatural resonance frequency is represented by an approximate cubicfunction as shown in FIG. 17. And this temperature characteristic can beapproximated as formula (1) below.Y=α(t−t ₀)³β(t−t ₀)+γ  (1)Here, Y is an output frequency, α is a cubic coefficient, β is ainclination of a temperature characteristic, γ is a frequency offset,and to is a central temperature of a curve, that is, an inflection point(normally, a range from 25 to 30° C.). Each of α, β and γ of the aboveformula (1) greatly depends on the crystal resonator.

For this reason, temperature compensation has been conventionallyperformed by using an output voltage from an approximate cubic functiongenerating device as described in U.S. Pat. No. 3,233,946 for instance.

To be more specific, as shown in FIG. 18, the output of the approximatecubic function generating device for generating the approximate cubicfunction is supplied to a voltage-controlled crystal oscillator (VCXO)as a control voltage for compensating for the temperature characteristicof crystal, the device using a voltage V_(IN) outputted from atemperature detecting circuit for outputting a voltage changingprimarily against the temperature change as an input signal.

A voltage-frequency characteristic of the voltage-controlled crystaloscillation circuit widely applied at present can be approximated by alinear function. Therefore, the frequency characteristic against thetemperature of the crystal resonator can be approximated by a voltagecharacteristic against the temperature as shown in FIG. 19.

A voltage-temperature characteristic of the control voltage will be asin the following formula (2).f(t)=a ₃(t−t ₀)³ +a ₁(t−t ₀)+a ₀  (2)To be more specific, the voltage matching the control voltage in formula(2) is generated by the approximate cubic function generating device andis inputted to the voltage-controlled crystal oscillator so as tocompensate for the temperature characteristic of the crystal resonator.

However, a frequency-temperature characteristic of the crystal resonatorincludes an order component larger than a cubic component. Therefore,there is a difference between an approximate cubic function and data sothat, even if the control voltage capable of strictly compensating forthe approximate cubic function is generated, this difference remains asan element for being incapable of temperature compensation.

To solve this, it is possible to approximate the temperaturecharacteristic of the crystal resonator with a function of a higherorder and control the voltage-controlled crystal oscillator with avoltage of a function of a high order corresponding thereto so as toreduce the difference.

For instance, in the case of approximating frequency-temperaturecharacteristic data on one crystal resonator with a cubic function, thedifference between an approximate expression and the data is 0.320 ppmat the maximum in a temperature range of −30 to 85° C. If this isapproximated with a function of a fourth order, it becomes 0.130 ppm.And if further approximated with a function of a fifth order, it becomes0.126 ppm. It is thus possible to adjust the coefficient and generatethe control voltage by using a device for generating the functions ofhigher orders so as to perform the temperature compensation with ahigher order of accuracy.

As for a circuit for outputting a signal proportional to the functionscubic or of higher orders so far, a function generating device shown inFIG. 1 of Japanese Patent Laid-Open No. 8-116214 is known for instance.

The signal outputted from this circuit can be represented as apolynomial such as formula (3) below which is a general expression.$\begin{matrix}\begin{matrix}{{f(x)} = {{a_{n}x^{n}} + {a_{n - 1}x^{n - 1}} + \ldots + {a_{2}x^{2}} + {a_{1}x} + a_{0}}} \\{= {{a_{n}^{\prime}\left( {x - x_{0}} \right)}^{n} + \ldots + {a_{1}^{\prime}\left( {x - x_{0}} \right)} + a_{0}^{\prime}}}\end{matrix} & (3)\end{matrix}$For instance, an output signal of a fourth order function generatingdevice can be represented by formula (4) below. $\begin{matrix}\begin{matrix}{{f(x)} = {{a_{4}x^{4}} + {a_{3}x^{3}} + {a_{2}x^{2}} + {a_{1}x} + a_{0}}} \\{= {{a_{4}^{\prime}\left( {x - x_{0}} \right)}^{4} + {a_{2}^{\prime}\left( {x - x_{0}} \right)}^{2} + {a_{1}\left( {x - x_{0}} \right)} + a_{0}^{\prime}}}\end{matrix} & (4)\end{matrix}$However,a_(4′)=a₄a₂′=a₂−6a₄x₀ ², a₁′=a₁+2a₂x₀−8a₄x₀ ³, a₀′=a₀+a₁x₀+a₂x₀ ²−3a₄x₀⁴, x₀=−a₃/(4a₄)

As for the approximate fourth order function generating device, it ispossible, by using x₀ as in the above formula (4), to omit an n−1^(st)term, that is a cubic term and also reduce a circuit size.

However, the conventional example has an unsolved problem that it isdifficult to implement the circuit for generating the control voltagewith a configuration as in the formula (4).

The unsolved problem will be described by using a concrete example. Ifthe frequency-temperature characteristic data on one crystal resonatoris described first as a formula having the cubic term omitted as theformula (4), to representing the inflection point of this functionbecomes −149° C. to significantly exceed the normally compensated rangeof −30 to 85° C. A significant deviation of to means that the circuitmust have a wide input range of a functional circuit for generating thecontrol voltage equivalent thereto and must be the circuit having thetemperature outside an adjustment range taken into consideration. FIG.20 shows the order components, where it is understandable that, whilethe frequency-temperature characteristic of one crystal resonator iswithin ±10 ppm, the order components have the functions a significantdeflection width of ±1500 ppm at the maximum added thereto. Therefore,to compensate for the frequency-temperature characteristic of thecrystal resonator, the adjustment range of the coefficients a₄′ to a₀′of the orders must be wide for the control voltage, and the circuit forimplementing this becomes very disadvantageous as a dynamic range.Consequently, there arise the problems of significant increase in noiseand expansion of the circuit size due to extension of the controlvoltage from the cubic function to the function of the fourth order.Thus, it is not practical even when considering a merit of obtaining ahigher order of accuracy.

Consequently, the present invention has been implemented by noting theunsolved problems of the conventional example. And an object thereof isto provide the circuit capable of accurately providing high ordercomponents which are cubic or of higher orders and an accuratelyadjustable crystal oscillator using the function generating devicethereof for the temperature compensation.

DISCLOSURE OF THE INVENTION

A k-th order component generating circuit according to claim 1 of thepresent invention is characterized by comprising: a plurality i (i is aninteger of 5 or more) of differential amplifiers for having a commonlinear input signal inputted to one input terminal, having a constantlevel signal of a predetermined level inputted to the other inputterminal, outputting an reversed or non-reversed signal to the linearinput signal and having a limiter function of limiting an output signalto predetermined maximum and minimum values; and a constant level signalgenerating circuit for providing the constant level signal to each ofthe i differential amplifiers, wherein: first, second and thirddifferential amplifiers of the i differential amplifiers are set to havethe constant level signals at increasingly higher levels inputted inorder; the output signals of the first and third differential amplifiersand those of the second differential amplifier are set to be of mutuallyreverse polarity; a fourth differential amplifier of the i differentialamplifiers has the constant level signal to be inputted set as thesignal at the same level as the constant level signal to be inputted tothe second differential amplifier, and has the output signal thereof setto be of the same polarity as the output signals of the first and thirddifferential amplifiers and also has a range of the input signal to bethe maximum value and the input signal to be the minimum value setlarger than that of the second differential amplifier; each of (i−4)differential amplifiers other than the first, second, third and fourthdifferential amplifiers of the i differential amplifiers has theconstant level signal to be inputted set to be either lower than a levelof the constant level signal to be inputted to the first differentialamplifier or higher than a level of the constant level signal to beinputted to the third differential amplifier, and the output signals ofthe (i−4) differential amplifiers and those of the second differentialamplifier are set to be of mutually reverse polarity, thus constitutedto form the output signal of the component of a k-th order function (kis an odd number of 3 or more) on adding up the output signals of thefirst, second, third and (i−4) differential amplifiers; and the fourthdifferential amplifier is constituted to form the output signal of alinear component for offsetting the linear component of the n-th orderfunction component so as to generate the component of the k-th orderfunction including no linear component by adding the output signals ofthe i differential amplifiers.

According to this, it is possible, by adjusting energization currents ofthe (i−4) differential amplifiers, to form the output signal of ainclination more precipitous against the input signal in the range inwhich the input signal is larger than the maximum value or smaller thanthe minimum value so as to generate an approximate k-th order function(k is an odd number of 3 or more) with high accuracy.

The cubic order component generating circuit according to claim 2 of thepresent invention is characterized by being set as i=5 and k=3 in claim1.

Thus, it is possible to constitute a cubic-specific circuit out of thecircuits for generating an odd-numbered component of k-th order so as tooutput a cubic function with high accuracy.

The cubic order component generating circuit according to claim 3 of thepresent invention is characterized in that, in claim 2, a fifthdifferential amplifier has the constant level signal to be inputted setto be lower than the level of the constant level signal to be inputtedto the first differential amplifier and also has the range of the inputsignal to be the maximum value and the input signal to be the minimumvalue set smaller than that of the first differential amplifier.

Thus, it is possible to output the cubic function with high accuracy inthe case of expanding a range of input voltage only to a higher sidefrom an inflection point of the input voltage.

The cubic order component generating circuit according to claim 4 of thepresent invention is characterized in that the fifth differentialamplifier has the constant level signal to be inputted set to be higherthan the level of the constant level signal to be inputted to the thirddifferential amplifier and also has the range of the input signal to bethe maximum value and the input signal to be the minimum value setsmaller than that of the third differential amplifier.

Thus, it is possible to output the cubic function with high accuracy inthe case of expanding the range of input voltage only to a lower sidefrom the inflection point of the input voltage.

The third order component generating circuit according to claim 5 of thepresent invention is characterized by being set as i=6 and k=5 in claim1.

Thus, it is possible to constitute a circuit specialized in fifth orderout of the circuits for generating an odd-numbered component of k-thorder so as to output a fifth order function with high accuracy.

A fifth order component generating circuit according to claim 6 of thepresent invention is characterized in that, in claim 5, the fifthdifferential amplifier has the constant level signal to be inputted setto be lower than the level of the constant level signal to be inputtedto the first differential amplifier and also has the range of the inputsignal to be the maximum value and the input signal to be the minimumvalue set smaller than that of the first differential amplifier, and thesixth differential amplifier has the constant level signal to beinputted set to be higher than the level of the constant level signal tobe inputted to the third differential amplifier and also has the rangeof the input signal to be the maximum value and the input signal to bethe minimum value set smaller than that of the third differentialamplifier.

Thus, it is possible to output the fifth order function with highaccuracy in the case of expanding the range of input voltage only to ahigher side from an inflection point.

An m-th order component generating circuit according to claim 7 of thepresent invention is characterized by comprising: a plurality j (j is aninteger of 4 or more) of differential amplifiers for having a commonlinear input signal inputted to one input terminal, having a constantlevel signal of a predetermined level inputted to the other inputterminal, outputting an reversed or non-reversed signal to the linearinput signal and having a limiter function of limiting an output signalto predetermined maximum and minimum values; and a constant signaloutputting circuit for outputting a constant output signal; a constantlevel signal generating circuit for providing the constant level signalto each of the j differential amplifiers, wherein: first, second, thirdand fourth differential amplifiers of the j differential amplifiers areset to have the constant level signals at increasingly higher levelsinputted in order; the output signals of the first and seconddifferential amplifiers and those of the third and fourth differentialamplifiers are set to be of mutually reverse polarity, thus constitutedto form the output signal of the component of an m-th order function (mis an even number of 4 or more) on adding up the output signals of the jdifferential amplifiers; and the constant signal outputting circuit isconstituted to form the output signal of a 0-th order component foroffsetting the 0-th order component of the m-th order function componentso as to generate the component of the m-th order function including no0-th order component by adding the output signals of the j differentialamplifiers and the constant signal outputting circuit.

Thus, it is possible to generate an even-numbered component of m-thorder including no 0-th order component with high accuracy.

The m-th order component generating circuit according to claim 8 of thepresent invention is characterized in that, in claim 7, j is an evennumber of 6 or more, and each of (j−4) differential amplifiers otherthan the first, second, third and fourth differential amplifiers of thej differential amplifiers has the constant level signal to be inputtedset to be either lower than a level of the constant level signal to beinputted to the first differential amplifier or higher than a level ofthe constant level signal to be inputted to the fourth differentialamplifier.

Thus, it is possible, by adjusting energization currents of the (j−4)differential amplifiers, to form the output signal of a inclination moreprecipitous against the input signal in the range in which the inputsignal is larger than the maximum value or smaller than the minimumvalue so as to generate an approximate m-th order function with highaccuracy.

The fourth order component generating circuit according to claim 9 ofthe present invention is characterized by being set as j=4 and m=4 inclaim 7.

Thus, it is possible to constitute a circuit specialized in the fourthorder out of the circuits for generating an even-numbered component ofm-th order so as to output a fourth order function with high accuracy.

An approximate n-th order function generating device according to claim10 of the present invention is characterized by comprising: a 0-th ordercomponent generating portion for having a constant signal inputted andgenerating a constant component; a linear component generating portionfor having a linear input signal inputted and generating a linearcomponent; at least one k-th order component generating portion having ak-th order component (k is an odd number of 3 or more) generatingcircuit for having the linear input signal inputted and a first variablegain amplifying circuit for having an output signal of the k-th ordercomponent generating circuit inputted; at least one m-th order componentgenerating portion having an m-th order component (m is an even numberof 4 or more) generating circuit for having the linear input signalinputted and a second variable gain amplifying circuit for having anoutput signal of the m-th order component generating circuit inputted;and an adding circuit for adding the output signals of the 0-th ordercomponent generating portion, the linear component generating portion,the k-th order component generating portion and the m-th order componentgenerating portion, wherein an approximate n-th order function (n is aninteger of 4 or more) is generated.

Thus, it is possible to render the cubic component main by omitting asecond order term and use an inflection point x₀ close to the inflectionpoint thereof. It is also possible, as the component of n-th order inn≧4 other than cubic becomes smaller, to use the common inflection pointx₀ as a configuration and implement the configuration of offset+linearcomponent+cubic component+corrective high order component so thatinfluence on a circuit size can be reduced.

An approximate n-th order function generating device according to claim11 of the present invention is characterized by comprising: a 0-th ordercomponent generating portion for having a constant signal inputted andgenerating a constant component; a linear component generating portionfor having a linear input signal inputted and generating a linearcomponent; at least one k-th order component generating portion having ak-th order component (k is an odd number of 3 or more) generatingcircuit according to claim 1 for having the linear input signal inputtedand a first variable gain amplifying circuit for having an output signalof the k-th order component generating circuit inputted; at least onem-th order component generating portion having an m-th order component(m is an even number of 4 or more) generating circuit according to claim7 for having the linear input signal inputted and a second variable gainamplifying circuit for having an output signal of the m-th ordercomponent generating circuit inputted; and an adding circuit for addingthe output signals of the 0-th order component generating portion, thelinear component generating portion, the k-th order component generatingportion and the m-th order component generating portion, wherein anapproximate n-th order function (n is an integer of 4 or more) isgenerated.

Thus, it is possible to render the cubic component capable of accurategeneration main by omitting the second order term and use the inflectionpoint x₀ close to the inflection point thereof. It is also possible, asthe component of n-th order in n≧4 other than cubic becomes smaller, touse the common inflection point x₀ as the configuration and implementthe configuration of offset+linear component+cubic component+correctivehigh order component so that the influence on the circuit size can bereduced.

An approximate cubic function generating device according to claim 12 ofthe present invention is characterized by comprising: a 0-th ordercomponent generating portion for having a constant input signal inputtedand generating a constant component; a linear component generatingportion for having a linear input signal inputted and generating alinear component; a cubic component generating portion having a cubiccomponent generating circuit according to either claim 2 or claim 4 forhaving the linear input signal inputted and a first variable gainamplifying circuit for having an output signal of the cubic componentgenerating circuit inputted; and an adding circuit for adding the outputsignals of the 0-th order component generating portion, the linearcomponent generating portion and the cubic component generating portion.

Thus, it is possible to generate an approximate cubic function with highaccuracy.

An approximate fourth order function generating device according toclaim 13 of the present invention is characterized by comprising: a 0-thorder component generating portion for having a constant input signalinputted and generating a constant component; a linear componentgenerating portion for having a linear input signal inputted andgenerating a linear component; a cubic component generating portionhaving a cubic component generating circuit according to either claim 2or claim 4 for having the linear input signal inputted and a firstvariable gain amplifying circuit for having an output signal of thecubic component generating circuit inputted; a fourth order componentgenerating portion having a fourth order component generating circuitaccording to claim 9 for having the linear input signal inputted and asecond variable gain amplifying circuit for having an output signal ofthe fourth order component generating circuit inputted; and an addingcircuit for adding the output signals of the fourth order componentgenerating portion, the cubic component generating portion, the linearcomponent generating portion and the 0-th order component generatingportion.

Thus, it is possible to generate an approximate fourth order functionwith high accuracy.

An approximate fifth order function generating device according to claim14 of the present invention is characterized by comprising: a 0-th ordercomponent generating portion for having a constant input signal inputtedand generating a constant component; a linear component generatingportion for having a linear input signal inputted and generating alinear component; a cubic component generating portion having a cubiccomponent generating circuit according to either claim 2 or claim 4 forhaving the linear input signal inputted and a first variable gainamplifying circuit for having an output signal of the cubic componentgenerating circuit inputted; a fourth order component generating portionhaving a fourth order component generating circuit according to claim 9for having the linear input signal inputted and a second variable gainamplifying circuit for having an output signal of the fourth ordercomponent generating circuit inputted; a fifth order componentgenerating portion having a fifth order component generating circuitaccording to claim 5 or 6 for having the linear input signal inputtedand a third variable gain amplifying circuit for having an output signalof the fifth order component generating circuit inputted; and an addingcircuit for adding the output signals of the fifth order componentgenerating portion, the fourth order component generating portion, thecubic component generating portion, the linear component generatingportion and the 0-th order component generating portion.

Thus, it is possible to generate an approximate fifth order functionwith high accuracy.

An approximate n-th order function generating device according to claim15 of the present invention is characterized by having the linear inputsignal inputted, outputting an n-th output signal proportional to ann-th order function represented by an n-th order polynomial andincluding no second order term in the n-th order polynomial.

Thus, it is possible to render the cubic component main and use theinflection point x₀ close to the inflection point thereof. It is alsopossible, as the component of n-th order in n≧4 other than cubic becomessmaller, to use the common inflection point x₀ as the configuration andimplement the configuration of offset+linear component+cubiccomponent+corrective high order component so that the influence on thecircuit size can be reduced.

A temperature function generating circuit according to claim 16 of thepresent invention is characterized by comprising a temperature detectingcircuit and the approximate n-th order function generating deviceaccording to claim 15 for having a detection signal of the temperaturedetecting circuit inputted.

Thus, it is possible to constitute the temperature function generatingcircuit capable of supplying the detection signal of the temperaturedetecting circuit as the input signal to the approximate n-th orderfunction generating device and generating a voltage capable ofcorrecting a temperature characteristic of crystal.

A temperature compensation crystal oscillation circuit according toclaim 17 of the present invention is characterized by comprising thetemperature function generating circuit according to claim 16 and acrystal oscillation circuit for having the approximate n-th orderfunction generated in the temperature function generating circuitinputted.

Thus, it is possible to constitute the temperature compensation crystaloscillation circuit capable of performing temperature compensation withhigh accuracy.

A temperature function generating circuit according to claim 18 of thepresent invention is characterized by comprising a temperature detectingcircuit and the approximate n-th order function generating deviceaccording to claim 10 or 11 for having a detection signal of thetemperature detecting circuit inputted.

Thus, it is possible to constitute the temperature function generatingcircuit capable of generating the voltage for correcting the temperaturecharacteristic of crystal by using the approximate n-th order functiongenerating device with high accuracy.

A temperature compensation crystal oscillation circuit according toclaim 19 of the present invention is characterized by comprising thetemperature function generating circuit according to claim 18 and acrystal oscillation circuit for having the approximate n-th orderfunction generated in the temperature function generating circuitinputted.

Thus, it is possible to constitute the temperature compensation crystaloscillation circuit capable of performing the temperature compensationwith high accuracy.

A temperature function generating circuit according to claim 20 of thepresent invention is characterized by comprising a temperature detectingcircuit and the approximate cubic function generating device accordingto claim 12 for having a detection signal of the temperature detectingcircuit inputted.

Thus, it is possible to constitute the temperature function generatingcircuit specialized in the cubic function.

A temperature compensation crystal oscillation circuit according toclaim 21 of the present invention is characterized by comprising thetemperature function generating circuit according to claim 20 and acrystal oscillation circuit for having the approximate cubic functiongenerated in the temperature function generating circuit inputted.

Thus, it is possible to constitute the temperature compensation crystaloscillation circuit specialized in the cubic function.

A temperature function generating circuit according to claim 22 of thepresent invention is characterized by comprising a temperature detectingcircuit and the approximate fourth order function generating deviceaccording to claim 13 for having a detection signal of the temperaturedetecting circuit inputted.

Thus, it is possible to constitute the temperature function generatingcircuit specialized in the fourth order function.

A temperature compensation crystal oscillation circuit according toclaim 23 of the present invention is characterized by comprising thetemperature function generating circuit according to claim 22 and acrystal oscillation circuit for having the approximate fourth orderfunction generated in the temperature function generating circuitinputted.

Thus, it is possible to constitute the temperature compensation crystaloscillation circuit specialized in the fourth order function.

A temperature function generating circuit according to claim 24 of thepresent invention is characterized by comprising a temperature detectingcircuit and the approximate fifth order function generating deviceaccording to claim 14 for having a detection signal of the temperaturedetecting circuit inputted.

Thus, it is possible to constitute the temperature function generatingcircuit specialized in the fifth order function.

A temperature compensation crystal oscillation circuit according toclaim 25 of the present invention is characterized by comprising thetemperature function generating circuit according to claim 24 and acrystal oscillation circuit for having the approximate fifth orderfunction generated in the temperature function generating circuitinputted.

Thus, it is possible to constitute the temperature compensation crystaloscillation circuit specialized in the fifth order function.

A temperature compensation adjustment method according to claim 26 ofthe present invention is characterized in that, when making atemperature compensation adjustment to a temperature compensationcrystal oscillation circuit comprised of a temperature compensationcircuit including a temperature detecting circuit and an approximaten-th order function generating device (n is an integer of 3 or more) anda voltage-controlled crystal oscillation circuit, a measurement is madeon an n-th order component VC_(OUTn) to a 0-th order component VC_(OUT0)of an output voltage VC_(OUT) of the temperature compensation circuit ina predetermined temperature atmosphere, and measurements are also made,at a plurality of temperatures in a desired temperature compensationrange, on an input voltage VC_(IN) at which an oscillating frequencyoutputted from the voltage-controlled crystal oscillation circuitmatches a preset selected frequency, and the n-th order componentVC_(OUTn) of the output voltage VC_(OUT) measured at each temperature isapproximated as a function of a temperature T by:VC _(OUTn)′(T)=VC _(OUTn)(T)−VC _(OUT0)(T),and the output voltage VC_(OUT) is described as a function of thetemperature T by:VC_(OUT)(T) = α_(n)VC_(OUTn)^(′)(T + Δ  T) + … + α₃VC_(OUT  3)^(′)(T + Δ  T) + α₁VC_(OUT  1)^(′)(T + Δ  T) + VC_(OUT  0)^(′)(T + Δ  T) + α₀,and coefficients α_(n) to α₃, α₁, α₀ and ΔT of the temperaturecompensation circuit are adjusted so that the input voltage VC_(IN) andoutput voltage VC_(OUT) measured at each of the temperatures arematching.

Thus, it is possible to obtain an effect of allowing the temperaturecompensation with high accuracy. In addition, it is possible to obtaindetailed and correct data by measuring the orders individually. And itis possible to calculate more optimal coefficients based on actual databy considering errors other than those of the components of the orders.Furthermore, it is possible to accurately adjust the temperaturecompensation by one temperature sweep not only on an approximate cubicfunction circuit but also on an approximate n-th function generatingcircuit in n≧4.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram showing an embodiment in the case of applyingthe present invention to a temperature compensation crystal oscillationcircuit.

FIG. 2 is a block diagram showing a concrete example of the temperaturecompensation crystal oscillation circuit to which an approximate fifthorder function generating device is applied.

FIG. 3 is a block diagram showing a concrete example of the temperaturecompensation crystal oscillation circuit to which an approximate fourthorder function generating device is applied.

FIG. 4 is a circuit diagram showing an example of an n-th componentgenerating portion in FIG. 1.

FIG. 5 is a circuit diagram showing an example of a fifth ordercomponent generating circuit applicable to FIG. 4.

FIG. 6 is a basic circuit diagram for explaining operation of the fifthorder component generating circuit in FIG. 5.

FIGS. 7A and 7B are characteristic diagrams showing outputcharacteristics of each differential pair for explaining the operationof a portion of the fifth order component generating circuit in FIG. 5.

FIG. 8 is an output waveform diagram of FIG. 5.

FIGS. 9A to 9D are output waveform diagrams for explaining the operationof the fifth order component generating circuit in FIG. 5.

FIG. 10 is a circuit diagram showing an example of the fourth ordercomponent generating circuit applicable to FIG. 4.

FIGS. 11A to 11D are output waveform diagrams for explaining theoperation of the fourth order component generating circuit in FIG. 10.

FIG. 12 is a circuit diagram showing a basic portion of a cubiccomponent generating circuit applicable to FIG. 4.

FIGS. 13A to 13E are output waveform diagrams for explaining theoperation of the basic portion of the cubic component generating circuitin FIG. 12.

FIG. 14 is a circuit diagram showing an example of the cubic componentgenerating circuit suitable in the case of expanding an input voltagerange.

FIGS. 15A to 15E are output waveform diagrams for explaining theoperation of the cubic component generating circuit in FIG. 14.

FIG. 16 is a block diagram showing a linear function generating portionapplicable to FIGS. 1 to 3.

FIG. 17 is a diagram showing a frequency characteristic against atemperature of a crystal resonator.

FIG. 18 is a block diagram showing a conventional example.

FIG. 19 is a diagram showing a temperature characteristic of controlvoltage to be inputted to a voltage-controlled crystal oscillator.

FIG. 20 is a characteristic diagram showing characteristics of aconventional approximate expression.

FIG. 21 is a characteristic diagram showing characteristics of anapproximate expression of the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereafter, embodiments of the present invention will be described basedon drawings.

First, a description will be given as to a principle of an approximaten-th order function generating device of the present invention.

An n-th order function may be generally represented as in formula (5)below. $\begin{matrix}\begin{matrix}{{f(x)} = {{a_{n}x^{n}} + {a_{n - 1}x^{n - 1}} + \ldots + {a_{3}x^{3}} + {a_{2}x^{2}} + {a_{1}x} + a_{0}}} \\{= {{a_{n}^{\prime}\left( {x - x_{0}} \right)}^{n} + {a_{n - 1}^{\prime}\left( {x - x_{0}} \right)}^{n - 1} + \ldots +}} \\{{a_{3}^{\prime}\left( {x - x_{0}} \right)}^{3} + {a_{1}^{\prime}\left( {x - x_{0}} \right)} + a_{0}^{\prime}}\end{matrix} & (5)\end{matrix}$As a concrete example, a fifth order function may be represented as informula (6) below. $\begin{matrix}\begin{matrix}{{f(x)} = {{a_{5}x^{5}} + {a_{4}x^{4}} + {a_{3}x^{3}} + {a_{2}x^{2}} + {a_{1}x} + a_{0}}} \\{= {{a_{5}^{\prime}\left( {x - x_{0}} \right)}^{5} + {a_{4}^{\prime}\left( {x - x_{0}} \right)}^{4} + {a_{3}^{\prime}\left( {x - x_{0}} \right)}^{3} + {a_{1}\left( {x - x_{0}} \right)} + a_{0}^{\prime}}}\end{matrix} & (6)\end{matrix}$

In this formula (6), relations among coefficients are as follows.

a₅′=a₅

a₄′=a₄+5a₅x₀

a₃′=a₃+4a₄x₀+10a₅x₀ ²

a₁′=a₁−3a₃x₀−8a₄x₀ ³−15a₅x₀ ⁴

a₀′=a₀+a₁x₀−2a₃x₀ ³−5a₄x₀ ⁴−9a₅x₀ ⁵

However, x₀ is a solution to the following cubic equation.10a ₅ x ₀ ³+6a ₄ x ₀ ²+3 a ₃ x ₀ +a ₂=0As for this x₀, one solution or three solutions can be obtained so thata value close to an assumed value should be selected x₀ in the formula(6) becomes “29” due to this conversion, which is approximately equal toan inflection point on approximating the same data to a cubic functionnear a center of a normally compensated temperature range. Therefore, itbecomes advantageous as a circuit configuration in that a cubiccomponent is a main component while fourth and fifth order componentsbecome smaller.

And a fourth order function may be represented as in formula (7) below.$\begin{matrix}\begin{matrix}{{f(x)} = {{a_{4}x^{4}} + {a_{3}x^{3}} + {a_{2}x^{2}} + {a_{1}x} + a_{0}}} \\{= {{a_{4}^{\prime}\left( {x - x_{0}} \right)}^{4} + {a_{3}^{\prime}\left( {x - x_{0}} \right)}^{3} + {a_{1}\left( {x - x_{0}} \right)} + a_{0}^{\prime}}}\end{matrix} & (7)\end{matrix}$In this formula (7), the relations among the coefficients are asfollows.a₄′=a₄a₃′=a₃+4a₄x₀a₁′=a₁−3a₃x₀ ²−8a₄x₀ ³a₀′=a₀+a₁x₀−2a₃x₀ ³−5a ₄ x ₀ ⁴However, x₀ is a solution to the following quadratic equation.6a ₄ x ₀ ²+3a ₃ x ₀ +a ₂=0As for this x₀, two solutions can be obtained so that a value closer tothe center of a curve should be selected. Consequently, x₀ is “31” whichis approximately equal to the inflection point on approximating the samedata to the cubic function near the center of the normally compensatedtemperature range. Furthermore, the orders when represented in formula(7) as described above can be illustrated as in FIG. 21 so that thefourth order component is within ±3 ppm. Thus, if represented in aformula having no second order component such as the formula (6) or (7),the main components are the cubic components and linear components andonly a few high order components having the inflection pointsapproximately equal to the inflection points of the cubic components areadded. It is a very advantageous configuration as a dynamic range of acircuit for generating control voltage equivalent to this.

FIG. 1 is a block diagram showing an embodiment of a temperaturecompensation crystal oscillation circuit according to the presentinvention.

In FIG. 1, reference numeral 1 denotes a temperature detecting circuitof which analog output voltage changes linear-functionally against atemperature change. And a detected temperature value due to an analogvoltage outputted from the temperature detecting circuit 1 is inputtedas an input signal V_(IN) to an approximate n-th order functiongenerating device 2 to generate a voltage for compensating a temperaturecharacteristic of crystal so as to supply it to a voltage-controlledcrystal oscillator (VCXO) 3.

Here, the approximate n-th order function generating device 2 generatesthe voltage represented by the n-th order function of the aforementionedformula (5). It has the input signal V_(IN) inputted, and based thereon,it is comprised of an n-th component generating portion 6 n forgenerating only the n-th component of a first term in the aforementionedformula (5), a cubic component generating portion 6B for generating onlythe cubic component of an n−2 term in formula (5), a linear componentgenerating portion 6A for generating only the linear component of an n−1term in formula (5) and an adding circuit 4 for adding output signals ofthe n-th component generating portion 6 n, cubic component generatingportion 6B and linear component generating portion 6A.

The approximate n-th order function generating device 2 can have n setat an arbitrary high order. For a concrete example, the temperaturecompensation crystal oscillation circuit is constituted by applying anapproximate fifth order function generating device 2A shown in FIG. 2 oran approximate fourth order function generating device shown in FIG. 3.

To be more specific, as to the temperature compensation crystaloscillation circuit in FIG. 2, the approximate fifth order functiongenerating device 2A has a fourth order component generating portion 6Cand a fifth order component generating portion 6D provided thereto inaddition to the adding circuit 4, 0-th order component generatingportion 5, linear component generating portion 6A and cubic componentgenerating portion 6B in the aforementioned configuration in FIG. 1,where the output signals of the linear component generating portion 6A,cubic component generating portion 6B, fourth order component generatingportion 6C and fifth order component generating portion 6D are added bythe adding circuit 4.

As for the temperature compensation crystal oscillation circuit in FIG.3, the approximate fourth order function generating device 2B isconstituted by omitting the fifth order component generating portion 6Din the configuration in FIG. 2.

As shown in FIG. 4, each of the cubic component generating portion 6B,fourth order component generating portion 6C, fifth order componentgenerating portion 6D . . . and n-th component generating portion 6 n inFIGS. 1 to 3 is comprised of an n-th component generating circuit 9 forgenerating only each order component of the cubic, fourth order, fifthorder . . . n-th order components, a variable gain amplifying circuit 11for having an output of the n-th component generating circuit 9 inputtedand a constant level signal generating circuit 20 for providing constantlevel signals V_(REFL1) to V_(REFH2) mentioned later to the n-thcomponent generating circuit 9.

Here, a fifth order component generating circuit will be described as anexample of an odd function. As shown in FIG. 5, the fifth ordercomponent generating circuit is comprised of a current mirror circuit 14comprising a MOS field-effect transistor Tr0 having a gate and a drainconnected to a positive power terminal VDD via a constant current source13 and having the source grounded to a VSS and six MOS field-effecttransistors Tr1 to Tr6 having their respective gates connected to thegate of the MOS field-effect transistor Tr0, six differential amplifiers15A to 15F constituting first to sixth amplifiers to which a constantcurrent is supplied from the current mirror circuit 14, resistances 16Aand 16B having the same resistance value for constituting an adder foradding output currents of the differential amplifiers 15A to 15F, and adifferential amplifier 12 for obtaining a current difference of theoutput. The differential amplifiers 15A to 15F are supplied withdifferent constant level reference voltages V_(REFH1), V_(REFH2),V_(REFM), V_(REFL2) and V_(REFL1) from the constant level signalgenerating circuit 20.

Here, the differential amplifier 15A has MOS field-effect transistorsTrA₁ and TrA₂ serially connected to the drain of the MOS field-effecttransistor Tr1 of the current mirror circuit 14 via resistances RA₁ andRA₂ respectively. The input signal V_(IN) is supplied to the gate of thetransistor TrA₁, and the constant level reference voltages V_(REFM) issupplied to the gate of the transistor TrA₂, and the drain of thetransistor TrA₁ is connected to the positive power terminal VDD via oneof the resistances 16A constituting the adder and an MOS field-effecttransistor 17 for receiving the output of the differential amplifier 12on its gate while the drain of the transistor TrA₂ is connected to thepositive power terminal VDD via the other resistance 16B constitutingthe adder.

Likewise, the differential amplifier 15B also has MOS field-effecttransistors TrB₁ and TrB₂ serially connected to the drain of the MOSfield-effect transistor Tr1 of the current mirror circuit 14 viaresistances RB₁ and RB₂ respectively. The input signal V_(IN) issupplied to the gate of the transistor TrB₁, and the constant levelreference voltages V_(REFM) is supplied to the gate of the transistorTrB₂. As is contrary to the aforementioned differential amplifier 15A,however, the drain of the transistor TrB₁ is connected to the positivepower terminal VDD via the other resistance 16B constituting the adderwhile the drain of the transistor TrB₂ is connected to the positivepower terminal VDD via the MOS field-effect transistor 17 and one of theresistances 16A constituting the adder so as to have reversecharacteristics to the other differential amplifiers 15A, 15C, 15D, 15Eand 15F.

The differential amplifiers 15C, 15D, 15E and 15F also have the sameconfiguration as the differential amplifier 15A, and have the constantlevel reference voltages V_(REFL1), V_(REFH1), V_(REFL2) and V_(REFH2)generated by the constant level signal generating circuit 20 inputtedrespectively. And the MOS field-effect transistors TrA₁, TrB₂, TrC₁,TrD₁, TrE₁ and TrF₁ are connected to the resistance 16A constituting theadder via the MOS field-effect transistor 17 with their connectionpoints connected to an inverting input side of the operational amplifier12.

Sizes of the constant level reference voltages V_(REFH1) to V_(REFL1)supplied to the differential amplifiers 15A to 15F are set asV_(REFH2)>V_(REFH1)>V_(REFM)>V_(REFL1)>V_(REFL2), and the differentialamplifier 15B also has the constant level reference voltage V_(REFM) ofthe same voltage as the differential amplifier 15A supplied thereto.

And a difference current between a normal rotation output currentI_(POUT) passing through the resistances 16A and 16B and an invertingoutput current I_(NOUT) passing through a ground VSS via the MOSfield-effect transistors TrA1 to TrF1, resistances RA₁ to RF₁ and MOSfield-effect transistors Tr1 to Tr6 of the differential amplifiers 15Ato 15F is outputted as an output current I_(OUT) from an output terminal18 of the fifth order component generating circuit. The output currentI_(OUT) is supplied to the inverting input side of an operationalamplifier OPA having a variable resistance VR inserted via a negativefeedback constituting the variable gain amplifying circuit 11. Aconstant voltage V_(OFF) generated by a constant voltage generatingcircuit 10 is supplied to a normal rotation input side of theoperational amplifier OPA, and it is possible to obtain an output V5_(OUT) of only the fifth order component including no linear componentas represented by formula (8) below.V5_(OUT) =B5(V _(IN) −V _(OFF))⁵  (8)Here, a coefficient B5 is determined by a gain of the fifth ordercomponent generating circuit and the gain of the variable gainamplifying circuit.

Next, operation of the fifth order component generating circuit will bedescribed.

To begin with, a description will be given as to one differentialamplifier 15C as shown in FIG. 6 in order to simplify the description ofcircuit operation of the fifth order component generating circuit. In astate in which an input voltage V_(IN) is sufficiently smaller than thereference voltages V_(REFL1), all the currents passing through the MOSfield-effect transistors Tr3 will pass through the MOS field-effecttransistors TrC₂.

For this reason, if a constant current value of the current mirrorcircuit 14 is I₀, it follows that a current passing through the MOSfield-effect transistor TrC₂ I_(C2)=I₀ and a current passing through theMOS field-effect transistor TrC₁ I_(C1)=0. Therefore, the currentI_(NOUT) and current I_(POUT) become I₀ and 0 as shown in broken lineand in full line in FIG. 7A.

From this state, if the input voltage V_(IN) increases and exceedsV_(CL) which is the constant level reference voltage V_(REFL1) minusI₀·RC₂ for a voltage drop at a resistance RC₂, an output current IC₂gradually and smoothly decreases. As opposed to it, an output currentIC₁ smoothly increases, and if the input voltage V_(IN) becomes equal tothe constant level reference voltage V_(REFL1), both the output currentsIC₁ and IC₂ become equal. If the input voltage V_(IN) further rises, theoutput current IC₂ maintains a decreasing trend and the output currentIC₁ maintains an increasing trend. And if it becomes equal to or exceedsV_(CH) which is the reference voltage V_(REFL1) plus I₀·RC₁ for thevoltage drop at a resistance RC₁, the output current IC₂ becomes 0 andthe output currents IC₁ becomes I₀ inversely.

After all, of output characteristics in FIG. 7B, there is only a smoothchange in the output near V_(REFL1)±I₀·RC as to the characteristic ofthe transistors determined only by the resistance values RC of theresistances RC₁ and RC₂ and constant current value I₀ of the currentmirror circuit 14.

Next, to simplify the description of the operation of the fifth ordercomponent generating circuit in FIG. 5, consideration is given to thecircuits excluding the differential amplifiers 15A, 15E and 15F. Whenthe input voltage V_(IN) is sufficiently smaller than the constant levelreference voltage V_(REFL1) (V_(IN)<<V_(REFL1)), all the currentspassing through the MOS field-effect transistors Tr3 will pass throughthe MOS field-effect transistors TrC₂ in the differential amplifier 15Cas previously mentioned so as to consequently become I_(C2)=I₀ andI_(C1)=0. Likewise, in the differential amplifiers 15B and 15D, itbecomes I_(B2)=I_(D2)=I₀, I_(B1)=I_(D1)=0 and added currents I_(POUT)=2I₀ and I_(NOUT)=I₀.

And if the input voltage V_(IN) increases, the current starts passingthrough the MOS field-effect transistor TrC₁ and the current passingthrough the MOS field-effect transistor TrC₂ starts decreasingaccordingly. If the input voltage V_(IN) reaches the constant levelreference voltage V_(REFL1), it becomes I_(C1)=I_(C2)=I₀/2. As the statedoes not change as to the other differential amplifiers 15B and 15D, theoutput currents I_(NOUT) and I_(POUT) consequently becomeI_(NOUT)=I_(POUT)=3 I₀/2. If the input voltage V_(IN) further rises, itbecomes I_(C2)=0 and I_(C1)=I₀ so that the output currents I_(POUT) andI_(NOUT) consequently become I_(POUT)=I₀ and I_(NOUT)=2 I₀.

If the input voltage V_(IN) further increases, the current startspassing through the MOS field-effect transistor TrB₁ of the differentialamplifier 15B and the current passing through the MOS field-effecttransistor TrB₂ starts decreasing. If the input voltage V_(IN) reachesthe constant level reference voltage V_(REFM), it becomesI_(B1)=I_(B2)=I₀/2. And the output currents I_(POUT) and I_(NOUT) becomeI_(NOUT)=I_(POUT)=3 I₀/2 again.

If the output voltage V_(IN) further increases after becoming I_(POUT)=2I₀ and I_(NOUT)=I₀, the current starts passing through the MOSfield-effect transistor TrD₁ of the differential amplifier 15D and thecurrent passing through the MOS field-effect transistor TrD₂ startsdecreasing. If the input voltage V_(IN) reaches the constant levelreference voltage V_(REFH1), the output currents I_(POUT) and I_(NOUT)become I_(POUT)=I_(NOUT)=3 I₀/2 again. And if the input voltage V_(IN)further increases, they become I_(POUT)=I₀ and I_(NOUT)=2 I₀.

Therefore, viewing the I_(NOUT) side for instance, the output currentI_(C1) of the third differential amplifier 15C maintains 0 until thevoltage of an input signal V_(IN) reaches a minimum value V_(CL) of thethird differential amplifier 15C, starts increasing on exceeding theminimum value V_(CL), becomes I₀/2 on reaching the constant levelreference voltage V_(REFL1), and also increases thereafter according toincrease in the voltage of an input signal V_(IN) so as to reach I₀ at amaximum value V_(CH) and become saturated as shown in dashed line inFIG. 8.

The output current I_(B2) of the second differential amplifier 15Bmaintains I₀ until the voltage of the input signal V_(IN) reaches aminimum value V_(BL) (set as an equal value to V_(CH) according to thisembodiment) of the second differential amplifier 15B, starts decreasingon exceeding the minimum value V_(BL), becomes I₀/2 on reaching theconstant level reference voltage V_(REFM), and also decreases thereafteraccording to increase in the voltage of the input signal V_(IN) so as tomaintain 0 at a maximum value V_(BH) or more as shown in broken line inFIG. 8.

Furthermore, the output current I_(D1) of the fifth differentialamplifier 15D maintains 0 until the voltage of the input signal V_(IN)reaches a minimum value V_(DL) (set as an equal value to V_(BH)according to this embodiment) of the fourth differential amplifier 15D,starts increasing on exceeding the minimum value V_(DL), becomes I₀/2 onreaching the constant level reference voltage V_(REFH1), and alsodecreases thereafter according to increase in the voltage of the inputsignal V_(IN) so as to reach I₀ and become saturated at a maximum valueV_(DH) as shown in full line in FIG. 8.

As the first differential amplifier 15A is not added at this point intime, a linear function of a negative inclination is added to an oddfunction.

Therefore, it is the same configuration as the differential amplifiers15C and 15D, where the linear function can be offset by adding theoutput current of the first differential amplifier 15A of which range ofa minimum value V_(AL) and a maximum value V_(AH) is widely set.

To be more specific, it is possible, by adjusting energization currentssupplied to the differential amplifier 15A and resistances RA₁ and RA₂and optimizing the area and inclination of a linear function area, tomatch the minimum value V_(AL) with V_(CL) of the third differentialamplifier 15D and also match the maximum value V_(AH) with the maximumvalue V_(CH) of the fourth differential amplifier 15D regardinginput-output characteristics as shown in chain double-dashed line inFIG. 8 so as to obtain the output current having no linear component.

Furthermore, the differential amplifier 15E of the same configuration asthe differential amplifier 15C is added. It is added for the sake ofaccurately implementing the characteristic of the fifth order function,because the fifth order function is characterized by, in the area of theinputs voltage V_(IN) very remote from the constant level referencevoltage V_(REFM), being the output having a significant inclinationagainst V_(IN).

To be more specific, it is possible, by setting the inputted constantlevel reference voltage V_(REFL2) at a value smaller than V_(REFL1)inputted to the differential amplifier 15C, to increase the energizationcurrent value and increase the resistance value so as to pass the outputcurrent of a more precipitous inclination to the input voltage V_(IN) inthe range in which the input voltage V_(IN) is smaller than the minimumvalue V_(CL). Likewise, it is possible, by setting the constant levelreference voltage V_(REFH2) inputted to the differential amplifier 15Fof the same configuration as the differential amplifier 15D at a valuelarger than V_(REFH1) inputted to the differential amplifier 15D, toincrease the energization current value and increase the resistancevalue so as to pass the output current of a more precipitous inclinationto the input voltage V_(IN) in the range in which the input voltageV_(IN) is larger than the maximum value V_(DH).

As described above, as for the output currents I_(OUT) of the fifthorder component generating circuit, the output of the differentialamplifier 15A is as shown in FIG. 9C, output addition of thedifferential amplifiers 15B, 15C and 15D is as shown in FIG. 9A, and theoutput addition of the differential amplifiers 15E and 15F is as shownin FIG. 9B. If the entirety is added, it becomes a smooth fifth orderfunction current output I_(OUT) as shown in FIG. 9D. Therefore, as shownin FIG. 4, if the constant voltage is supplied to the normal rotationinput side and the fifth order function current output I_(OUT) issupplied to the inverting input side of the operational amplifier OPAhaving the variable resistance VR inserted via the negative feedbackconstituting the variable gain amplifying circuit 11, it is possible toobtain the output V5 _(OUT) of only the fifth order component includingno linear component inverted from the operational amplifier OPA.

Thus, it is possible, by using the six differential amplifiers asdescribed above, to appropriately set circuit constants so as togenerate only the fifth order function including no linear component asin formula (9) below.V5_(OUT) =B5(V _(IN) −V _(REFM))⁵  (9)

This circuit configuration is also applicable to the odd function ofn-th order. Therefore, it is possible to appropriately set the values ofthe constant level reference voltages V_(REFL2) and V_(REFH2),resistance values RE₁, RE₂, RF₁ and RF₂ and the energization currentvalue inputted to the differential amplifiers 15E and 15F and furtheradd a plurality of differential amplifiers to optimize the resistancevalues, reference voltages and energization current value so as toobtain the output as in formula (10) below.Vn _(OUT) =Bn(V _(IN) −V _(REFM))^(n)  (10)

To be more specific, it should comprise: a plurality i (i is an integerof 5 or more) of differential amplifiers for having a common linearinput signal inputted to one input terminal, having a constant levelsignal of a predetermined level inputted to the other input terminal,outputting an reversed or non-reversed signal to the linear input signaland having a limiter function of limiting an output signal topredetermined maximum and minimum values; and a constant level signalgenerating circuit for providing the constant level signal to each ofthe i differential amplifiers, wherein: first, second and thirddifferential amplifiers of the i differential amplifiers are set to havethe constant level signals at increasingly higher levels inputted inorder; the output signals of the first and third differential amplifiersand those of the second differential amplifier are set to be of mutuallyreverse polarity; a fourth differential amplifier of the i differentialamplifiers has the constant level signal to be inputted set as thesignal at the same level as the constant level signal to be inputted tothe second differential amplifier, and has the output signal thereof setto be of the same polarity as the output signals of the first and thirddifferential amplifiers and also has a range of the input signal to bethe maximum value and the input signal to be the minimum value setlarger than that of the second differential amplifier; each of (i−4)differential amplifiers other than the first, second, third and fourthdifferential amplifiers of the i differential amplifiers has theconstant level signal to be inputted set to be either lower than a levelof the constant level signal to be inputted to the first differentialamplifier or higher than a level of the constant level signal to beinputted to the third differential amplifier, and the output signals ofthe (i−4) differential amplifiers and those of the second differentialamplifier are set to be of mutually reverse polarity, thus constitutedto form the output signal of the component of a k-th order function (kis an odd number of 7 or more) on adding up the output signals of thefirst, second, third and (i−4) differential amplifiers; and the fourthdifferential amplifier is constituted to form the output signal of alinear component for offsetting the linear component of the n-th orderfunction component so as to generate the component of the k-th orderfunction including no linear component by adding the output signals ofthe i differential amplifiers.

Next, a fourth order component generating circuit will be described asan example of an even function output circuit.

FIG. 10 shows an example of the fourth order component generatingcircuit.

The fourth order component generating circuit is comprised of thecurrent mirror circuit 14 comprising the MOS field-effect transistor Tr0having the gate and drain connected from the positive power terminal VDDvia the constant current source 13 and having the source grounded to theVSS and the five MOS field-effect transistors Tr1 to Tr5 having theirrespective gates connected to the gate of the MOS field-effecttransistor Tr0, the MOS field-effect transistor Tr6 constituting aconstant current source circuit to which the constant current issupplied from the current mirror circuit 14, and the resistances 16A and16B having the same resistance value as the adder for adding the outputcurrents of the differential amplifiers 15A to 15D and the constantcurrent source circuit. The differential amplifiers 15A to 15D aresupplied with different constant level reference voltages V_(REFH1),V_(REFH2), V_(REFL2) and V_(REFL1) generated by the constant levelsignal generating circuit 20.

Here, the differential amplifier 15A has MOS field-effect transistorsTrA₁ and TrA₂ serially connected to the drain of the MOS field-effecttransistor Tr1 of the current mirror circuit 14 via resistances RA₁ andRA₂ respectively. The input signal V_(IN) is supplied to the gate of thetransistor TrA₁, and the constant level reference voltages V_(REFL1) issupplied to the gate of the transistor TrA₂. The drain of the transistorTrA₁ is connected to the positive power terminal VDD via one of theresistances 16B constituting the adder while the drain of the transistorTrA₂ is connected to the positive power terminal VDD via the MOSfield-effect transistor 17 and the other resistance 16A constituting theadder.

And the differential amplifiers 15B, 15C and 15D have equalconfigurations in which the constant level reference voltages V_(REFH1),V_(REFL2) and V_(REFH2) generated by the constant level signalgenerating circuit 20 are supplied to the respective gates of thetransistors TrB₂, TrC₂ and TrD₂. However, the differential amplifiers15B and 15D are set to have reverse characteristics to the differentialamplifiers 15A and 15C.

The constant level reference voltages areV_(REFH2)>V_(REFH1)>V_(REFL1)>V_(REFL2), and the values of the currentspassing through the transistors TrC and TrD are set at larger valuesthan TrA and TrB, such as I_(A)=I_(B)=I₀, I_(C)=I_(D)=2 I₀ for instance.

As behavior of a single differential amplifier is the same as that inthe description as to the fifth order component generating circuit, theoutput I_(OUT) by the differential amplifiers 15A and 15B is as shown inFIG. 11A. Furthermore, the output by the differential amplifiers 15C and15D is as shown in FIG. 11B. These output currents are added andconverted to voltages by the variable resistance VR provided in FIG. 4so as to obtain the output of the fourth order function against theinput signal V_(IN).

When the input signal V_(IN) is at the inflection point x₀ of the fourthorder function, that is, between the constant level reference voltagesV_(REFL1) and V_(REFH1), the output current I_(OUT) becomesI_(OUT)=I_(POUT)−I_(NOUT)=2 I₀+I₀+I₀+2 I₀=6 I₀ so that it becomes the0-th order component of the output. Therefore, the circuit having 6 I₀supplied thereto as the constant current is added in order to offset the0-th order component. This can be created from the current mirrorcircuit 14 supplying the constant current to each of the differentialamplifiers 15A to 15D. At this time, it is possible to connect the otherresistance 16A constituting the adder to the MOS field-effecttransistors Tr1 to Tr5 of the current mirror circuit 14 via another MOSfield-effect transistor Tr6 inputting the input signal V_(IN) to thatgate so that a source-drain voltage of the MOS field-effect transistorsTr1 to Tr5 constituting the current mirror circuit 14 gets close to thesource-drain voltage of the other MOS field-effect transistor Tr6 so asto obtain a more accurate output.

The output currents from the constant current circuit are as shown inFIG. 11C. If all the current outputs are added up, a fourth orderfunction current output I_(OUT) as in FIG. 11D can be obtained. It ispossible to supply the, constant voltage V_(OFF) generated by theconstant voltage generating circuit 10 to the normal rotation input sideand also supply the current output I_(OUT) to the inverting input sideof the operational amplifier OPA having the variable resistance VRinserted via the negative feedback constituting the variable gainamplifying circuit 11 as shown in FIG. 4 so as to obtain an outputV4_(OUT) of only the fourth order component having inverted the currentoutput from the operational amplifier OPA.

Thus, it is possible to appropriately set the circuit constants by usingthe four differential amplifiers 15A to 15D and the constant currentcircuit as described above so as to generate only the fourth orderfunction including no 0-th order component as in formula (11) below.V4_(OUT) =B4(V _(IN) −V _(REFM))4  (11)

This circuit configuration is also applicable to the even function ofm-th order. And it is possible to appropriately set the values of theconstant level reference voltages V_(REFL1), V_(REFL2), V_(REFH1) andV_(REFH2), resistances RA₁ to RD₂ and the energization current valueinputted to the differential amplifiers 15A to 15D and further add aplurality of differential amplifiers to optimize the resistance values,constant level reference voltages and energization current value so asto obtain the output as in formula (12) below.Vm _(OUT) =Bm(V _(IN) −V _(REFM))^(m)  (12)

To be more specific, it should comprise: a plurality j (j is an integerof 4 or more) of differential amplifiers for having a common linearinput signal inputted to one input terminal, having a constant levelsignal of a predetermined level inputted to the other input terminal,outputting an reversed or non-reversed signal to the linear input signaland having a limiter function of limiting an output signal topredetermined maximum and minimum values; and a constant signaloutputting circuit for outputting a constant output signal; a constantlevel signal generating circuit for providing the constant level signalto each of the j differential amplifiers, wherein: first, second, thirdand fourth differential amplifiers of the j differential amplifiers areset to have the constant level signals at increasingly higher levelsinputted in order; the output signals of the first and seconddifferential amplifiers and those of the third and fourth differentialamplifiers are set to be of mutually reverse polarity, thus constitutedto form the output signal of the component of an m-th order function (mis an even number of 6 or more) on adding up the output signals of the jdifferential amplifiers; and the constant signal outputting circuit isconstituted to form the output signal of a 0-th order component foroffsetting the 0-th order component of the m-th order function componentso as to generate the component of the m-th order function including no0-th order component by adding the output signals of the j differentialamplifiers and the constant signal outputting circuit.

Next, a description will be given as to an improvement example of acubic component generating circuit in the case of extending thecompensated temperature range to be either higher or lower. Extension ofthe temperature range is equivalent to expanding the range of the outputvoltage from the temperature detecting circuit 1, that is, expanding therange of the input voltage of the cubic component generating circuit.

As shown in FIG. 12, the cubic component generating circuit known so faris comprised of the current mirror circuit 14 comprising the MOSfield-effect transistor Tr0 having a gate and a drain connected to apositive power terminal VDD via the constant current source 13 andhaving the source grounded to the VSS and four MOS field-effecttransistors Tr1 to Tr4 having their respective gates connected to thegate of the MOS field-effect transistor Tr0, four differentialamplifiers 15A to 15D constituting the first to fourth amplifiers towhich the constant current is supplied from the current mirror circuit14, and the resistances 16A and 16B having the same resistance value forconstituting the adder for adding the output currents of thedifferential amplifiers 15A to 15D. The differential amplifiers 15A to15D are supplied with different constant level reference voltagesV_(REFH), V_(REFM) and V_(REFL).

Here, the differential amplifier 15A has the MOS field-effecttransistors TrA₁ and TrA₂ serially connected to the drain of the MOSfield-effect transistor Tr1 of the current mirror circuit 14 viaresistances RA₁ and RA₂ respectively. The input signal V_(IN) issupplied to the gate of the transistor TrA₁, and the constant levelreference voltages V_(REFM) is supplied to the gate of the transistorTrA₂. The drain of the transistor TrA₁ is connected to the positivepower terminal VDD via one of the resistances 16A constituting the adderand an MOS field-effect transistor 17 for receiving the output of thedifferential amplifier 12 on its gate while the drain of the transistorTrA₂ is connected to the positive power terminal VDD via the otherresistance 16B constituting the adder.

Likewise, the differential amplifier 15B also has the MOS field-effecttransistors TrB₁ and TrB₂ serially connected to the drain of the MOSfield-effect transistor Tr1 of the current mirror circuit 14 via theresistances RB₁ and RB₂ respectively. The input signal V_(IN) issupplied to the gate of the transistor TrB₁, and the constant levelreference voltages V_(REFM) is supplied to the gate of the transistorTrB₂. As is contrary to the aforementioned differential amplifier 15A,however, the drain of the transistor TrB₁ is connected to the positivepower terminal VDD via the other resistance 16B constituting the adderwhile the drain of the transistor TrB₂ is connected to the positivepower terminal VDD via the MOS field-effect transistor 17 and one of theresistances 16A constituting the adder so as to have reversecharacteristics to the other differential amplifiers 15A, 15C and 15D.

The differential amplifiers 15C and 15D have equal configurations tothat of the differential amplifier 15A, provided that the input signalV_(IN) is supplied to the gates of the transistors TrC₁ and TrD₁belonging to them respectively, and the constant level referencevoltages V_(REFL) and V_(REFH) are supplied to the gates of thetransistors TrC₂ and TrD₂.

The output current I_(OUT) of the differential amplifier 15A is as shownin FIG. 13A, the output current I_(OUT) of the differential amplifier15B is as shown in FIG. 13B, the output current I_(OUT) of thedifferential amplifier 15C is as shown in FIG. 13C, and the outputcurrent I_(OUT) of the differential amplifier 15D is as shown in FIG.13D. As the entire output currents are the addition of the outputcurrents I_(OUT), the result is as shown in FIG. 13E. This outputcurrent is supplied to the inverting input side of the operationalamplifier OPA having the variable resistance VR inserted via thenegative feedback constituting the variable gain amplifying circuit 11,and the constant voltage is supplied to the normal rotation input sideof the operational amplifier OPA so as to obtain the output V3 _(OUT) ofonly the cubic component including no linear component as represented byformula (13) below.V3_(OUT) =B3(V _(IN) −V _(OFF)) ³  (13)Here, a coefficient B3 is determined by the gain of the cubic componentgenerating circuit and the gain of the variable gain amplifying circuit11.

However, in the case of extending the range of input voltage only to behigher as to the cubic component generating circuit for instance, theinput voltage V_(IN) significantly deviates from the cubic componentgenerating circuit at a place where it is high as shown in FIG. 13E. Itis because the output of the differential amplifier 15D becomessaturated.

For this reason, it is necessary to correct the output of thedifferential amplifier 15D to which the constant level reference voltageV_(REFH) is inputted.

Here, the differential amplifier 15E for inputting the constant levelreference voltage V_(REFH2) is added. The improved cubic componentgenerating circuit is shown in FIG. 14. However, it is set at theconstant level reference voltage V_(REFH2)>V_(REFH). It is possible tooffset the 0-th order component by setting energization currents I_(C0),I_(D0) and I_(E0) of the differential amplifiers 15C, 15D and 15E to beI_(C0)=I_(D0)+I_(E0).

First, the differential amplifiers 15A, 15B and 15C have the sameconfiguration so that their outputs will be as shown in FIGS. 15A, 15Band 15C respectively. And the output of the differential amplifier 15Dis as indicated in full line in FIG. 15D while the output of thedifferential amplifier 15E is as shown in FIG. 15D. It is possible, byadding the output current of the differential amplifier 15E near thepoint where the output of the differential amplifier 15D becomessaturated, to make a correction to significant deviation of the inputvoltage V_(IN) from the cubic component generating circuit at a placewhere it is high so that an output result of adding all will be as shownin FIG. 15E.

Thus, it is possible, by appropriately setting resistance values RD₁,RD₂, RF₁ and RF₂ and the constant level reference voltages V_(REFH) andV_(REFH2) of the respective amplifiers, to constitute the cubiccomponent generating circuit for obtaining a better cubic function onextending the range of the input voltage V_(IN) only to be higher.

As shown in FIG. 16, the linear component generating portion 6A iscomprised of the variable resistance VR connected between an inputterminal t_(IN) for having the input signal V_(IN) inputted and aconstant level reference voltage input terminal t_(R) and a normalrotation amplifier for having a slider of the variable resistance VRsupplied to the normal rotation input side, having the constant levelreference voltage input terminal t_(R) supplied to the inverting inputside via the resistance R₁ respectively and having the output signalsreturned to the inverting input side via the resistance R₂, where theconstant level reference voltage V_(REFM) of the cubic componentgenerating circuit is supplied to the reference voltage input terminalt_(R).

According to the linear component generating portion 6A, the inputsignal V_(IN) is amplified by a normal rotation amplifier 20, where anoutput voltage VB_(OUT) of the normal rotation amplifier 20 can berepresented by the following formula.VB _(OUT) =B1(V _(IN) −V _(REFM))  (14)

Here, a coefficient variable B1 is determined by a set value of thevariable resistance VR and the gain of the normal rotation amplifier 20.

The aforementioned FIG. 1 represents an example of the temperaturecompensation crystal oscillation circuit of the present invention. Acrystal resonator used therein has the temperature characteristic of anoscillating frequency against the temperature as shown in FIG. 17. Thischaracteristic can be generally represented by a polynomial such as aformula (15) below. $\begin{matrix}{Y = {{a_{n}\left( {t - t_{0}} \right)}^{n} + {a_{n - 1}\left( {t - t_{0}} \right)}^{n - 1} + \ldots + {a_{3}\left( {t - t_{0}} \right)}^{3} + {a_{1}\left( {t - t_{0}} \right)} + a_{0}}} & (15)\end{matrix}$

This characteristic relies on the characteristics of the crystalresonator and voltage-controlled crystal oscillation circuit. Avoltage-frequency characteristic of the voltage-controlled crystaloscillation circuit widely applied at present can be approximated by alinear function. Therefore, the frequency characteristic against thetemperature of the crystal resonator can be implemented by a voltagecharacteristic against the temperature. Therefore, in the embodiment inFIG. 1, it is possible to generate the voltage equivalent to the termson the right-hand side of formula (15) with the approximate n-th orderfunction generating device 2 based on a temperature detection signal ofthe temperature detecting circuit 1, perform a gain adjustment as toindividual variations among coefficients a₀ to a_(n) of each order withthe variable gain amplifying circuit 11 in each n-th order componentgenerating portion, perform a fine adjustment, add the voltages afterthe fine adjustment with the adding circuit, and obtain the controlvoltage of the voltage-controlled crystal oscillation circuitcorresponding to the frequency characteristic against the temperature ofthe crystal resonator so as to supply the control voltage to avoltage-controlled crystal oscillation circuit 3 and thereby correctlycompensate for temperature dependence of the crystal resonator includedtherein.

To be more precise, the approximate n-th order function generatingdevice 2 and a voltage-controlled crystal oscillator (VCXO) 3 in FIG. 1are separately stored in a thermostatic oven of which temperature isthen set at an arbitrary temperature t₁ within a range desired toperform temperature compensation. With the temperature of thethermostatic oven stably set at the preset temperature t₁, an inputvoltage VC_(IN) of the voltage-controlled crystal oscillator 3 ischanged to measure an input voltage VC_(IN)(t₁) of which frequency ofthe output signal is the frequency matching a preset frequency and alsomeasure an output voltage VC_(OUTn)(t₁) of the approximate n-th orderfunction generating device 2 as to each individual order. To be morespecific, a strict measurement is performed by setting the gains of theother order components to be zero and rendering the output of only onecomponent obtainable. Thus, n-th order to cubic data and linear and 0-thorder data are taken as the output voltages of the approximate n-thorder function generating device 2.

The above measurement process is repeated a plurality of times whilesequentially changing the preset temperature of the thermostatic oven soas to measure the input voltages VC_(IN)(t₁) to VC_(IN)(t_(m)) of thevoltage-controlled crystal oscillator 3 and also measure the outputvoltages VC_(OUT1)(t₁) to VC_(OUTm)(t_(m)) of the approximate n-th orderfunction generating device 2 at the preset temperatures (t₁ to t_(m))Next, the output voltages VC_(OUTn)(t₁) to VC_(OUTn)(t_(m)) of theapproximate n-th order function generating device 2 minus the respective0-th order components VC_(OUTn)(t₁) to VC_(OUTn)(t_(m)) are approximatedto a function of the temperature as in formula (16) below. This isbecause, as the output voltage VC_(OUTn) of the approximate n-th orderfunction generating device 2 includes the 0-th order component VC_(OUTn)generated by the 0-th order component generating portion, the 0-th ordercomponent (offset) should be subtracted to obtain a more correct n-thorder component VC_(OUTn) and allow a more accurate adjustment. In thiscase, there is no limit to the approximated function and it may bearbitrarily determined according to the data. The data on the orders isindividually taken so as to increase information for the adjustment andallow highly accurate adjustment.VC _(OUTn)′(t)≡VC _(OUTn)(t)−VC _(OUT0)(t)  (16)

Thereafter, the temperature compensation is performed by adjusting thecoefficients a_(n) to a₀ and Δt so that a function VC_(OUT)(t) shown informula (17) below matches the measured input voltages VC_(IN)(t₁) toVC_(IN)(t_(m)) at each of the temperatures. $\begin{matrix}{{{VC}_{OUT}(t)} = {{\alpha_{n}{{VC}_{OUTn}^{\prime}\left( {t + {\Delta\quad t}} \right)}} + \ldots + {\alpha_{3}{{VC}_{{OUT}\quad 3}^{\prime}\left( {t + {\Delta\quad t}} \right)}} + {\alpha_{1}{{VC}_{{OUT}\quad 1}^{\prime}\left( {t + {\Delta\quad t}} \right)}} + {{VC}_{{OUT}\quad 0}^{\prime}\left( {t + {\Delta\quad t}} \right)} + \alpha_{0}}} & (17)\end{matrix}$

To be more precise, a gain adjustment to obtain the coefficient a_(n) isperformed by the variable gain amplifying circuit 11 provided to then-th order component generating portion, and the 0-th order component isadjusted by adding a constant voltage value for obtaining thecoefficient a₀ at the adding circuit. The correction value Δt isadjusted by adjusting the offset of the temperature detecting circuit 1.

It is possible to measure the input voltage VC_(IN) of thevoltage-controlled crystal oscillator 3 and temperature compensationcircuit output voltages, that is, the output voltages VC_(OUTn) toVC_(OUT0) of each order of the approximate n-th order functiongenerating device 2 respectively and adjust the approximate n-th orderfunction generating device 2 based on these measurement results so as toperform highly accurate temperature compensation by performingtemperature sweep work just once.

As is understandable from the above, it is easy, by using a descriptionsuch as the aforementioned formula (5), to implement the approximaten-th order function generating device for generating the output voltageof that function. And it is also easy to adjust the above configurationin the case of using it as a temperature compensation circuit of thecrystal oscillator for instance. It is also possible, as to both the oddfunctions and even functions, to design the respective order componentgenerating devices of the above configuration with high accuracy. And itis possible, by using the above adjustment method, to adjust not onlythe approximate cubic function generating devices known so far but alsothe approximate n-th order function generating device 2 in n≧4 withhigher accuracy.

Likewise, it is also possible to perform the same adjustment method asabove to the temperature compensation crystal oscillation circuit towhich the approximate fifth order function generating device 2A shown inFIG. 2 is applied so as to perform highly accurate temperaturecompensation to the temperature compensation crystal oscillation circuitspecialized in the approximate fifth order function.

Furthermore, it is possible to perform the same adjustment method asabove to the temperature compensation crystal oscillation circuit towhich the approximate fourth order function generating device 2B shownin FIG. 3 is applied so as to perform the highly accurate temperaturecompensation to the temperature compensation crystal oscillation circuitspecialized in the approximate fourth order function.

The embodiments were described as to the cases of using the MOSfield-effect transistors on the approximate n-th order functiongenerating circuits. However, they are not limited thereto but it isalso possible to apply another active element such as a bipolartransistor.

The embodiments were described as to the cases of a ground standard.However, they are not limited thereto but it is also possible to adopt aVDD standard.

Furthermore, the embodiments were described as to the cases where theoutput from each order component generating device is the currentoutput. However, they are not limited thereto but it is also possible,as a matter of course, to adopt a voltage output.

INDUSTRIAL APPLICABILITY

It is possible to generate the n-th order function with high accuracy byadopting the n-th order function generating device and perform thetemperature compensation with high accuracy by applying the n-th orderfunction generating device to the temperature compensation crystaloscillation circuit.

It becomes possible to perform the temperature compensation with highaccuracy by adopting the temperature compensation adjustment method. Inaddition, it is possible to obtain detailed and correct data bymeasuring the orders individually. And it is possible to calculate moreoptimal coefficients based on actual data by considering errors otherthan those of the components of the orders. Furthermore, it is feasibleto accurately adjust the temperature compensation by one temperaturesweep not only in the approximate cubic function generating portionknown so far but also in the approximate n-th function generatingportion in n≧4.

1. A k-th order component generating circuit, characterized bycomprising: a plurality i (i is an integer of 5 or more) of differentialamplifiers for having a common linear input signal inputted to one inputterminal, having a constant level signal of a predetermined levelinputted to the other input terminal, outputting an reversed ornon-reversed signal to the linear input signal and having a limiterfunction of limiting an output signal to predetermined maximum andminimum values; and a constant level signal generating circuit forproviding the constant level signal to each of the i differentialamplifiers, wherein: first, second and third differential amplifiers ofthe i differential amplifiers are set to have the constant level signalsat increasingly higher levels inputted in order, and the output signalsof the first and third differential amplifiers and those of the seconddifferential amplifier are set to be of mutually reverse polarity; afourth differential amplifier of the i differential amplifiers has theconstant level signal to be inputted set as the signal at the same levelas the constant level signal to be inputted to the second differentialamplifier, and has the output signal thereof set to be of the samepolarity as the output signals of the first and third differentialamplifiers and also has a range of the input signal to be the maximumvalue and the input signal to be the minimum value set larger than thatof the second differential amplifier; each of (i−4) differentialamplifiers other than the first, second, third and fourth differentialamplifiers of the i differential amplifiers has the constant levelsignal to be inputted set to be either lower than a level of theconstant level signal to be inputted to the first differential amplifieror higher than a level of the constant level signal to be inputted tothe third differential amplifier, and the output signals of the (i−4)differential amplifiers and those of the second differential amplifierare set to be of mutually reverse polarity; and thus constituted to formthe output signal of the component of a k-th order function (k is an oddnumber of 3 or more) on adding up the output signals of the first,second, third and (i−4) differential amplifiers; and the fourthdifferential amplifier is constituted to form the output signal of alinear component for offsetting the linear component of the k-th orderfunction component so as to generate the component of the k-th orderfunction including no linear component by adding the output signals ofthe i differential amplifiers.
 2. The cubic order component generatingcircuit according to claim 1, characterized by being set as i=5 and k=3.3. The cubic order component generating circuit according to claim 2,characterized in that a fifth differential amplifier has the constantlevel signal to be inputted set to be lower than the level of theconstant level signal to be inputted to the first differential amplifierand also has the range of the input signal to be the maximum value andthe input signal to be the minimum value set smaller than that of thefirst differential amplifier.
 4. The cubic order component generatingcircuit according to claim 2, characterized in that the fifthdifferential amplifier has the constant level signal to be inputted setto be higher than the level of the constant level signal to be inputtedto the third differential amplifier and also has the range of the inputsignal to be the maximum value and the input signal to be the minimumvalue set smaller than that of the third differential amplifier.
 5. Thefifth order component generating circuit according to claim 1,characterized by being set as i=6 and k=5.
 6. The fifth order componentgenerating circuit according to claim 5, characterized in that the fifthdifferential amplifier has the constant level signal to be inputted setto be lower than the level of the constant level signal to be inputtedto the first differential amplifier and also has the range of the inputsignal to be the maximum value and the input signal to be the minimumvalue set smaller than that of the first differential amplifier, and thesixth differential amplifier has the constant level signal to beinputted set to be higher than the level of the constant level signal tobe inputted to the third differential amplifier and also has the rangeof the input signal to be the maximum value and the input signal to bethe minimum value set smaller than that of the third differentialamplifier.
 7. An m-th order component generating circuit, characterizedby comprising: a plurality j (j is an integer of 4 or more) ofdifferential amplifiers for having a common linear input signal inputtedto one input terminal, having a constant level signal of a predeterminedlevel inputted to the other input terminal, outputting an reversed ornon-reversed signal to the linear input signal and having a limiterfunction of limiting an output signal to predetermined maximum andminimum values; and a constant signal outputting circuit for outputtinga constant output signal; a constant level signal generating circuit forproviding the constant level signal to each of the j differentialamplifiers, wherein: first, second, third and fourth differentialamplifiers of the j differential amplifiers are set to have the constantlevel signals at increasingly higher levels inputted in order; theoutput signals of the first and second differential amplifiers and thoseof the third and fourth differential amplifiers are set to be ofmutually reverse polarity; and thus constituted to form the outputsignal of the component of an m-th order function (m is an even numberof 4 or more) on adding up the output signals of the j differentialamplifiers; and the constant signal outputting circuit is constituted toform the output signal of a 0-th order component for offsetting the 0-thorder component of the m-th order function component so as to generatethe component of the m-th order function including no 0-th ordercomponent by adding the output signals of the j differential amplifiersand the constant signal outputting circuit.
 8. The m-th order componentgenerating circuit according to claim 7, characterized in that j is aneven number of 6 or more, and each of (j−4) differential amplifiersother than the first, second, third and fourth differential amplifiersof the j differential amplifiers has the constant level signal to beinputted set to be either lower than a level of the constant levelsignal to be inputted to the first differential amplifier or higher thana level of the constant level signal to be inputted to the fourthdifferential amplifier.
 9. The fourth order component generating circuitaccording to claim 7, characterized by being set as j=4 and m=4.
 10. Anapproximate n-th order function generating device, characterized bycomprising: a 0-th order component generating portion for having aconstant signal inputted and generating a constant component; a linearcomponent generating portion for having a linear input signal inputtedand generating a linear component; at least one k-th order componentgenerating portion having a k-th order component (k is an odd number of3 or more) generating circuit for having the linear input signalinputted and a first variable gain amplifying circuit for having anoutput signal of the k-th order component generating circuit inputted;at least one m-th order component generating portion having an m-thorder component (m is an even number of 4 or more) generating circuitfor having the linear input signal inputted and a second variable gainamplifying circuit for having an output signal of the m-th ordercomponent generating circuit inputted; and an adding circuit for addingthe output signals of the 0-th order component generating portion, thelinear component generating portion, the k-th order component generatingportion and the m-th order component generating portion, wherein anapproximate n-th order function (n is an integer of 4 or more) isgenerated.
 11. An approximate n-th order function generating device,characterized by comprising: a 0-th order component generating portionfor having a constant signal inputted and generating a constantcomponent; a linear component generating portion for having a linearinput signal inputted and generating a linear component; at least onek-th order component generating portion having a k-th order component (kis an odd number of 3 or more) generating circuit according to claim 1for having the linear input signal inputted and a first variable gainamplifying circuit for having an output signal of the k-th ordercomponent generating circuit inputted; at least one m-th order componentgenerating portion having an m-th order component (m is an even numberof 4 or more) generating circuit according to claim 7 for having thelinear input signal inputted and a second variable gain amplifyingcircuit for having an output signal of the m-th order componentgenerating circuit inputted; and an adding circuit for adding the outputsignals of the 0-th order component generating portion, the linearcomponent generating portion, the k-th order component generatingportion and the m-th order component generating portion, wherein anapproximate n-th order function (n is an integer of 4 or more) isgenerated.
 12. An approximate cubic function generating device,characterized by comprising: a 0-th order component generating portionfor having a constant input signal inputted and generating a constantcomponent; a linear component generating portion for having a linearinput signal inputted and generating a linear component; a cubiccomponent generating portion having a cubic component generating circuitaccording to either claim 2 or claim 4 for having the linear inputsignal inputted and a first variable gain amplifying circuit for havingan output signal of the cubic component generating circuit inputted; andan adding circuit for adding the output signals of the 0-th ordercomponent generating portion, the linear component generating portionand the cubic component generating portion.
 13. An approximate fourthorder function generating device, characterized by comprising: a 0-thorder component generating portion for having a constant input signalinputted and generating a constant component; a linear componentgenerating portion for having a linear input signal inputted andgenerating a linear component; a cubic component generating portionhaving a cubic component generating circuit according to either claim 2or claim 4 for having the linear input signal inputted and a firstvariable gain amplifying circuit for having an output signal of thecubic component generating circuit inputted; a fourth order componentgenerating portion having a fourth order component generating circuitaccording to claim 9 for having the linear input signal inputted and asecond variable gain amplifying circuit for having an output signal ofthe fourth order component generating circuit inputted; and an addingcircuit for adding the output signals of the fourth order componentgenerating portion, the cubic component generating portion, the linearcomponent generating portion and the 0-th order component generatingportion.
 14. An approximate fifth order function generating device,characterized by comprising: a 0-th order component generating portionfor having a constant input signal inputted and generating a constantcomponent; a linear component generating portion for having a linearinput signal inputted and generating a linear component; a cubiccomponent generating portion having a cubic component generating circuitaccording to either claim 2 or claim 4 for having the linear inputsignal inputted and a first variable gain amplifying circuit for havingan output signal of the cubic component generating circuit inputted; afourth order component generating portion having a fourth ordercomponent generating circuit according to claim 9 for having the linearinput signal inputted and a second variable gain amplifying circuit forhaving an output signal of the fourth order component generating circuitinputted; a fifth order component generating portion having a fifthorder component generating circuit according to claim 5 or 6 for havingthe linear input signal inputted and a third variable gain amplifyingcircuit for having an output signal of the fifth order componentgenerating circuit inputted; and an adding circuit for adding the outputsignals of the fifth order component generating portion, the fourthorder component generating portion, the cubic component generatingportion, the linear component generating portion and the 0-th ordercomponent generating portion.
 15. An approximate n-th order functiongenerating device, characterized by having the linear input signalinputted, outputting an n-th output signal proportional to an n-th orderfunction represented by an n-th order polynomial and including no secondorder term in the n-th order polynomial.
 16. A temperature functiongenerating circuit, characterized by comprising a temperature detectingcircuit and the approximate n-th order function generating deviceaccording to claim 15 for having a detection signal of the temperaturedetecting circuit inputted.
 17. A temperature compensation crystaloscillation circuit, characterized by comprising the temperaturefunction generating circuit according to claim 16 and a crystaloscillation circuit for having the approximate n-th order functiongenerated in the temperature function generating circuit inputted.
 18. Atemperature function generating circuit, characterized by comprising atemperature detecting circuit and the approximate n-th order functiongenerating device according to claim 10 or 11 for having a detectionsignal of the temperature detecting circuit inputted.
 19. A temperaturecompensation crystal oscillation circuit, characterized by comprisingthe temperature function generating circuit according to claim 18 and acrystal oscillation circuit for having the approximate n-th orderfunction generated in the temperature function generating circuitinputted.
 20. A temperature function generating circuit, characterizedby comprising a temperature detecting circuit and the approximate cubicfunction generating device according to claim 12 for having a detectionsignal of the temperature detecting circuit inputted.
 21. A temperaturecompensation crystal oscillation circuit, characterized by comprisingthe temperature function generating circuit according to claim 20 and acrystal oscillation circuit for having the approximate cubic functiongenerated in the temperature function generating circuit inputted.
 22. Atemperature function generating circuit, characterized by comprising atemperature detecting circuit and the approximate fourth order functiongenerating device according to claim 13 for having a detection signal ofthe temperature detecting circuit inputted.
 23. A temperaturecompensation crystal oscillation circuit, characterized by comprisingthe temperature function generating circuit according to claim 22 and acrystal oscillation circuit for having the approximate fourth orderfunction generated in the temperature function generating circuitinputted.
 24. A temperature function generating circuit, characterizedby comprising a temperature detecting circuit and the approximate fifthorder function generating device according to claim 14 for having adetection signal of the temperature detecting circuit inputted.
 25. Atemperature compensation crystal oscillation circuit, characterized bycomprising the temperature function generating circuit according toclaim 24 and a crystal oscillation circuit for having the approximatefifth order function generated in the temperature function generatingcircuit inputted.
 26. A temperature compensation adjustment method,characterized in that, when making a temperature compensation adjustmentto a temperature compensation crystal oscillation circuit comprised of atemperature compensation circuit including a temperature detectingcircuit and an approximate n-th order function generating device (n isan integer of 3 or more) and a voltage-controlled crystal oscillationcircuit, a measurement is made on an n-th order component VC_(OUTn) to a0-th order component VC_(OUT0) of an output voltage VC_(OUT) of thetemperature compensation circuit in a predetermined temperatureatmosphere, and measurements are also made, at a plurality oftemperatures in a desired temperature compensation range, on an inputvoltage VC_(IN) at which an oscillating frequency outputted from thevoltage-controlled crystal oscillation circuit matches a preset selectedfrequency, and the n-th order component VC_(OUTn) of the output voltageVC_(OUT) measured at each temperature is approximated as a function of atemperature T by:VC _(OUTn)′(T)=VC _(OUTn)(T)−VC _(OUT0)(T), and the output voltageVC_(OUT) is described as a function of the temperature T by:VC_(OUT)(T) = α_(n)VC_(OUTn)^(′)(T + Δ  T) + … + α₃VC_(OUT  3)^(′)(T + Δ  T) + α₁VC_(OUT  1)^(′)(T + Δ  T) + VC_(OUT  0)^(′)(T + Δ  T) + α₀,and coefficients α_(n) to α₃, α₁, α₀ and ΔT of the temperaturecompensation circuit are adjusted so that the input voltage VC_(IN) andthe output voltage VC_(OUT) measured at each of the temperatures arematching.